Hans Brodersen

• Brodersen, Hans & Skutlaberg, Olav (2010). A_0-sufficiency of jets from R^2 to R^2. The Journal of Singularities.  ISSN 1949-2006.  2, s 19- 51 . doi: 10.5427/jsing.2010.2b
• Brodersen, Hans (2009). Sufficiency of jets with line singularities. Bulletin of the London Mathematical Society.  ISSN 0024-6093.  41, s 445- 457 . doi: 10.1112/blms/bdp016
• Brodersen, Hans (2007). On sufficiency of jets, In Jean-Paul Brasselet; James Damon; Dung Trang Le & Matsuo Oka (ed.),  Singularities in geometry and topology; Proceedings of the Singularity Summer School and Workshop Trieste, August 15-September 3, 2005.  World Scientific.  ISBN 978-981-270-022-3.  artikkel.  s 585 - 597
• Brodersen, Hans (1998). Sufficiency of jets with respect to $\scr L$-equivalence, In T. Fukuda; T. Fukui; S. Izumiya & S. Koike (ed.),  Real analytic and algebraic singularities.  Longman.  ISBN 0-582-32874-8.  artikkel.  s 78 - 83
• Brodersen, Hans (1997). On finite and infinite $C\sp k$-$\scr A$-determinacy. Proceedings of the London Mathematical Society.  ISSN 0024-6115.  75(3), s 369- 435
• Brodersen, Hans; Ishikawa, Goo & Wilson, Leslie (1997). A criterion for finite topological determinacy of map-germs. Proceedings of the London Mathematical Society.  ISSN 0024-6115.  74(3), s 662- 700
• Brodersen, Hans (1983). A note on sufficient and nonsufficient jets. Journal of the London Mathematical Society.  ISSN 0024-6107.  27(2), s 167- 175
• Brodersen, Hans (1981). A note on infinite determinacy of smooth map germs. Bulletin of the London Mathematical Society.  ISSN 0024-6093.  13, s 397- 402
• Brodersen, Hans & Trotman, David (1979). Whitney ${\rm (}b)$-regularity is weaker than Kuo's ratio test for real algebraic stratifications. Mathematica Scandinavica.  ISSN 0025-5521.  45, s 27-34

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• Brodersen, Hans (2012). Sufficiency of jets.
• Brodersen, Hans (2010). Sufficiency of jets from the plane to the plane.
• Brodersen, Hans (2006). Sufficiency of jets from the plane to the plane.
• Brodersen, Hans (2005). Sufficiency of jets with isolated line singularities.
• Brodersen, Hans (1999). Determinacy of smooth map-germs. Show summary

  %\documentstyle{amsppt} \magnification=1200 \hsize=6.5 truein \vsize=9.0 truein \define\jet#1#2#3{j^{#1}{#2}({#3})} \define\R#1{{\Bbb R}^{#1}} \define\avb#1#2#3{{#1}:(\R{#2},0)\rightarrow(\R{#3},0)} \define\glatt{\ck {\infty}} \def\kimer{m_nC_{n,p}} \define\ck#1{C^{#1}} \topmatter \document \centerline {\bf Determinacy of smooth map germs}\vskip 4mm \centerline{Hans Brodersen} \centerline{University of Oslo}\vskip 4mm Let $C_{n,p}$ be the set of $\glatt$ map-germs from $(\R n,0)$ to $\R p$, and $m_nC_{n,p}$ the subset of germs mapping 0 to 0. Let $\Cal A$ be the group of germs of diffeomorphisms $(h,k)$ where $\avb hnn$ and $\avb kpp$. $\Cal A$ acts on $\kimer$ by the formula $(k,h)f=k\circ f\circ h^{-1}$. We say that $f$ is $r$-determined if any $g$ with $\jet rg0=\jet rf0$ (here $\jet rg0$ denotes the $r$-th order Taylor expansion of $g$ at 0) is in $f$\rq s $\Cal A$-orbit. Looking at the formal Taylor series $\jet\infty f0$ of $f$, we define the notion of infinite determinacy in a similar manner. In fact given any equivalence relation on $\kimer$ we can define the notion of finite/infinite determinacy with respect to this relation. We can forexample let $(h,k)$ above be homeomorphisms and condsider determinacy under topological equivalence.\par The foundations of the study of finitely $\Cal A$-determined germs was laid by John Mather in an important series of paper examining the properties of the $\glatt$-stable mappings. Here Mather gave sufficient and necessary coditions for finite determinacy. We will review Mather\rq s results and then discuss similar conditions characterizing infinite $\Cal A$-determinacy and finite determinacy with respect to topological equivalence.\par \end

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